I agree with greatnan about straight talking to the overseas sons, in a letter as whenim64 suggests. Although be careful of how you phrase things as they might show your aunt the letter. Also it is probably the case that sons tend to empathise less about caring needs, it is probably way down on their list of concerns - 'out of sight, out of mind' even though they purport to be 'grateful from a distance'. The thing is, what is to be done?
When the next crisis occurs - as it surely will do, you, nanaej will be the closest on hand and be able and expected to get to your aunt well before either of the sons can get flights. If, god forbid your aunt has a fall, you will be in the hospital, waiting with her. As you are not next of kin how does the hospital deal with you? What if power of attorney needs to be set up? Before your aunt goes into a care home (if she does), she may need carers going in to the flat (with all the problems that ensue from that).
For your own sake this needs to be sorted out now. You are not being unreasonable to be disappointed with the sons at all. They need to wake up and come back to the UK for a meeting, acknowledging that their mother can no longer drive. They need to talk to her GP and get an assessment of needs, they need to get a shift on.
The trouble is, many old people think they are fine and can manage forever.
I have experience of this, my sister and me for years now have taken responsibility for our aunt (although she has no children, there is only us) and although she is in care now, it has taken up a lot of our time - most of which we gladly give, but we live miles away and any visit or incident that needs to be dealt with takes up a whole day. Sometimes our aunt is a bit 'hard work' and we come away from a visit or previously doing some jobs in her home feeling wrung-out. Our parents died years ago, our dad looked after our mum before she died and our dad was ill for about a year and we saw to his every need.